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Lattice Boltzmann Schemes with Relative Velocities

Published online by Cambridge University Press:  30 April 2015

François Dubois,
Tony Fevrier and
Benjamin Graille
François Dubois
Affiliation:
CNAM Paris, Laboratoire de mécanique des structures et des systèmes couplés, FranceUniv. Paris-Sud, Laboratoire de mathématiques, UMR 8628, Orsay, F-91405, CNRS, Orsay, F-91405, France
Tony Fevrier*
Affiliation:
Univ. Paris-Sud, Laboratoire de mathématiques, UMR 8628, Orsay, F-91405, CNRS, Orsay, F-91405, France
Benjamin Graille
Affiliation:
Univ. Paris-Sud, Laboratoire de mathématiques, UMR 8628, Orsay, F-91405, CNRS, Orsay, F-91405, France
*
*Corresponding author. Email addresses: Francois.Dubois@math.u-psud.fr (F. Dubois), Tony.Fevrier@math.u-psud.fr (T. Fevrier), Benjamin.Graille@math.u-psud.fr (B. Graille)

Abstract

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In this contribution, a new class of lattice Boltzmann schemes is introduced and studied. These schemes are presented in a framework that generalizes the multiple relaxation times method of d’Humières. They extend also the Geier’s cascaded method. The relaxation phase takes place in a moving frame involving a set of moments depending on a given relative velocity field. We establish with the Taylor expansion method that the equivalent partial differential equations are identical to the ones obtained with the multiple relaxation times method up to the second order accuracy. The method is then performed to derive the equivalent equations up to third order accuracy.

Keywords

41A6065N7502.60CbLattice Boltzmann schemes with relative velocitiesequivalent equations methodcascaded D2Q9 scheme

Information

Type
Research Article
Information
Communications in Computational Physics , Volume 17 , Issue 4 , April 2015, pp. 1088 - 1112
Copyright
Copyright © Global-Science Press 2015 

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